A Text-Book On the Mechanics of Materials, And of Beams, Columns, And Shafts
A Text-Book On the Mechanics of Materials, And of Beams, Columns, And Shafts
Mansfield Merriman
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f Art. 42. BEAMS OVERHANGING BOTH SUPPORTS. 91 Fig. 35. Art. 42. Beams Overhanging Both Supports. When a beam overhangs both supports the bending moments for sections beyond the supports are negative, and in general between the supports there \vill be two inflection points. If the lengths m and n be . equal the reactions will be 5^^^^!^ ' >h--«-H equal under uniform load, each being one half of the total load. In any case, . whatever be the nature of the load,^the reactions may be found by the ...principle of moments (Art. 16), and then the vertical shears and bending moments may be deduced for all sections, after which the formulas (3) and (4) can be used for any special problem. Under a uniformly distributed load, and w = «, which is the most important practical case, each reaction is wm + ^/, the maximum shears at the supports are wm and ^/, the maxi- mum moment at the nyddle is + Mi'* "* i^')» ^^ maximum moment at each support is — iwm^, and the inflection points are distant J VP — 4m* from the middle of the beam.
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